Page 44 - Mechanical Engineers' Handbook (Volume 2)

1 Introduction 33

1. Dimming of the headlights while starting a car
2. Slowdown of an electric mixer lowered into heavy batter
3. Freezing a showerer by starting the dishwasher
4. Speedup of a vacuum cleaner when the hose plugs
5. Two-minute wait for a fever thermometer to rise
6. Special connectors required for TV antennas
7. Speedup of a fan in the window with the wind against it
8. Shifting of an automatic transmission on a hill
These effects happen because one part of a system loads another. Most mechanical
engineers would guess that weighing an automobile by placing a bathroom-type scale under
its wheels one at a time and summing the four measurements will yield a higher result than
would be obtained if the scale was flush with the floor. Most electrical engineers understand
that loading a potentiometer’s wiper with too low a resistance makes its dial nonlinear for
voltage division. Instrumentation engineers know that a heavy accelerometer mounted on a
thin panel will not measure the true natural frequencies of the panel. Audiophiles are aware
that loudspeaker impedances must be matched to amplifier impedance. We have all seen the
75- and 300- markings under the antenna connections on TV sets, and most cable sub-
scribers have seen balun transformers for connecting a coaxial cable to the flat-lead terminals
of an older TV.
Every one of these examples involves a desired or undesirable interaction between a
source and a receiver of energy. In every case, there are properties of the source part and
the load part of the system that determine the efficiency of the interaction. This chapter deals
exclusively with interactions between static and dynamic subsystems intended to function
together in a task and with how best to configure and characterize those subsystems.
Consider the analysis of dynamic systems. To create mathematical models of these
systems requires that we idealize our view of the physical world. First, the system must be
identified and separated from its environment. The environment of a system is the universe
outside the free body, control volume, or isolated circuit. The combination of these, which
is the system under study and the external sources, provides or removes energy from the
system in a known way. Next, in the system itself, we must arrange a restricted set of ideal
elements connected in a way that will correctly represent the energy storages and dissipations
of the physical system while, at the same time, we need the mathematical handles that
explore the system’s behavior in its environment. The external environment of the system
being modeled must then itself be modeled and connected and is usually represented by
special ideal elements called sources.
We expect, as a result of these sources, that the system under study will not alter the
important variables in its environment. The water rushing from a kitchen faucet will not
normally alter the atmospheric pressure; our electric circuit will not measurably slow the
turbines in the local power plant; the penstock will not draw down the level of the reservoir
(in a time frame consistent with a study of penstock dynamics, anyway); the cantilever beam
will not distort the wall it is built into; and so on. In this last instance, for example, the wall
is a special source of zero displacement and zero rotation no matter what forces and moments
are applied.
In this chapter, we consider, instead of the behavior of a single system in a known
environment, the interaction between pairs of connected dynamic systems at their interface,
often called the driving point. The fundamental currency is, as always, the energy or power
exchanged through the interface. In an instrumentation or control system, the objective of